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2 years ago

Y=3x+14 2x-3y=-14 Substitution method

Mathematics

2 answers:

riadik2000 [5.3K]2 years ago

5 0

X=-8

I know it’s that so it’s does not need a explanation

Montano1993 [528]2 years ago

4 0

Answer:

x = -8

Step-by-step explanation:

y = 3x + 14

2x - 3y = -14

So, what is the substitution? Y of course, this is because y is equal to 3x + 14.

2x - 3 (3x + 14) = -14

Multiply 3 with the numbers in the parentheses.

2x - 9x + 42 = -14

So you maybe be wondering why it is a negative 7 instead of subtracting 9 with 2. Using PEMDAS, we always read from left to right. So it is basically 2 -9 and you get -7.

-7x + 42 = -14

Then subtract 42 from both sides.

-7x + 42 - 42 = -14 - 42

Simplify

-7x = -56

Divide 7 by both sides.

-7x / 7 = -56 / 7

x = -8

And you might ask, why we get x instead afterwards. This is because both -7 and 7 cancel each other out leaving us with x.

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<h3>to understand this</h3><h3>you need to know about:</h3>

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To find the inverse, we swap the variables y and x, then solve for the new y.

3a. $y=\frac{3}{x-1}$

Swapping the variables: $x=\frac{3}{y-1}$
Solving for y: $x(y-1)=3 \\ y-1= \frac{3}{x} \\ y=1+\frac{3}{x}$
The domain of this inverse is $x ≠ 0$ .
3b. $y=x^2-1$

Swapping: $x = y^2 - 1$
Solving for y: $y^2 = x + 1 \\ y = \sqrt{x+1}$
The domain of this inverse is $x ≥ -1$ .
3c. $y=\sqrt[3]{\frac{x-7}{3}}$
Swapping: $x=\sqrt[3]{\frac{y-7}{3}}$
Solving for y: $x^3=\frac{y-7}{3} \\ y-7=3x^3 \\ y=3x^3+7$
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4a. $y=\frac{3}{x-1}$ , $y=1+\frac{3}{x}$
$y=\frac{3}{(1+\frac{3}{x})-1} \\ y=\frac{3}{(\frac{3}{x})} \\ y=x$
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4c. $y=\sqrt[3]{\frac{x-7}{3}}$ , $y=3x^3+7$
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